The purpose of the research is to examine the nonlinear relationship between stock prices and cash dividends based on the empirical data of 16 American firms classified as the category of Oil, Gas and Consumable Fuels Industry in S&P 500 index. The interval of dataset is 16 years so that the set is formed as a 16x16 panel and the empirical activities proceed as Panel Smooth Transition derived by Gonzalez, Terasvirta and Dijk (2004, 2005). The results show that there are only two regimes on the nonlinear relationship between stock price, cash dividend and quick ratis by the threshold parameter of debt ratio. Stock prices are positive relevant to cash dividends wherever the threshold parameter locates on but to quick ratio only when debt ratio exceeds 31.05%, negative relevant to quick ratio otherwise though. In the other case, we use returns on asset as the threshold parameter to detect the nonlinear relationship between the same endogenous and extraneous variables. The output represents that there exists two thresholds. Cash dividends are positive relevant to stock prices globally, especially on the second regime. On the other hand, when ROA is under 0.0451 or between 0.0451 and 0.1056, quick ratio is negative relevant to stock price. Moreover, quick ratio represents positive effect on stock price under the situation of ROA exceeds 0.1056.